# Solve using the Square Root Property 13x+1=14x^2

13x+1=14×2
Subtract 14×2 from both sides of the equation.
13x+1-14×2=0
Factor the left side of the equation.
Factor -1 out of 13x+1-14×2.
Reorder the expression.
Move 1.
13x-14×2+1=0
Reorder 13x and -14×2.
-14×2+13x+1=0
-14×2+13x+1=0
Factor -1 out of -14×2.
-(14×2)+13x+1=0
Factor -1 out of 13x.
-(14×2)-(-13x)+1=0
Rewrite 1 as -1(-1).
-(14×2)-(-13x)-1⋅-1=0
Factor -1 out of -(14×2)-(-13x).
-(14×2-13x)-1⋅-1=0
Factor -1 out of -(14×2-13x)-1(-1).
-(14×2-13x-1)=0
-(14×2-13x-1)=0
Factor.
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=14⋅-1=-14 and whose sum is b=-13.
Factor -13 out of -13x.
-(14×2-13x-1)=0
Rewrite -13 as 1 plus -14
-(14×2+(1-14)x-1)=0
Apply the distributive property.
-(14×2+1x-14x-1)=0
Multiply x by 1.
-(14×2+x-14x-1)=0
-(14×2+x-14x-1)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
-((14×2+x)-14x-1)=0
Factor out the greatest common factor (GCF) from each group.
-(x(14x+1)-(14x+1))=0
-(x(14x+1)-(14x+1))=0
Factor the polynomial by factoring out the greatest common factor, 14x+1.
-((14x+1)(x-1))=0
-((14x+1)(x-1))=0
Remove unnecessary parentheses.
-(14x+1)(x-1)=0
-(14x+1)(x-1)=0
-(14x+1)(x-1)=0
Multiply each term in -(14x+1)(x-1)=0 by -1
Multiply each term in -(14x+1)(x-1)=0 by -1.
(-(14x+1)(x-1))⋅-1=0⋅-1
Simplify (-(14x+1)(x-1))⋅-1.
Simplify by multiplying through.
Apply the distributive property.
(-(14x)-1⋅1)(x-1)⋅-1=0⋅-1
Multiply.
Multiply 14 by -1.
(-14x-1⋅1)(x-1)⋅-1=0⋅-1
Multiply -1 by 1.
(-14x-1)(x-1)⋅-1=0⋅-1
(-14x-1)(x-1)⋅-1=0⋅-1
(-14x-1)(x-1)⋅-1=0⋅-1
Expand (-14x-1)(x-1) using the FOIL Method.
Apply the distributive property.
(-14x(x-1)-1(x-1))⋅-1=0⋅-1
Apply the distributive property.
(-14x⋅x-14x⋅-1-1(x-1))⋅-1=0⋅-1
Apply the distributive property.
(-14x⋅x-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1
(-14x⋅x-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply x by x by adding the exponents.
Move x.
(-14(x⋅x)-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1
Multiply x by x.
(-14×2-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1
(-14×2-14x⋅-1-1x-1⋅-1)⋅-1=0⋅-1
Multiply -1 by -14.
(-14×2+14x-1x-1⋅-1)⋅-1=0⋅-1
Rewrite -1x as -x.
(-14×2+14x-x-1⋅-1)⋅-1=0⋅-1
Multiply -1 by -1.
(-14×2+14x-x+1)⋅-1=0⋅-1
(-14×2+14x-x+1)⋅-1=0⋅-1
Subtract x from 14x.
(-14×2+13x+1)⋅-1=0⋅-1
(-14×2+13x+1)⋅-1=0⋅-1
Apply the distributive property.
-14×2⋅-1+13x⋅-1+1⋅-1=0⋅-1
Simplify.
Multiply -1 by -14.
14×2+13x⋅-1+1⋅-1=0⋅-1
Multiply -1 by 13.
14×2-13x+1⋅-1=0⋅-1
Multiply -1 by 1.
14×2-13x-1=0⋅-1
14×2-13x-1=0⋅-1
14×2-13x-1=0⋅-1
Multiply 0 by -1.
14×2-13x-1=0
14×2-13x-1=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=14⋅-1=-14 and whose sum is b=-13.
Factor -13 out of -13x.
14×2-13x-1=0
Rewrite -13 as 1 plus -14
14×2+(1-14)x-1=0
Apply the distributive property.
14×2+1x-14x-1=0
Multiply x by 1.
14×2+x-14x-1=0
14×2+x-14x-1=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(14×2+x)-14x-1=0
Factor out the greatest common factor (GCF) from each group.
x(14x+1)-(14x+1)=0
x(14x+1)-(14x+1)=0
Factor the polynomial by factoring out the greatest common factor, 14x+1.
(14x+1)(x-1)=0
(14x+1)(x-1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
14x+1=0
x-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
14x+1=0
Subtract 1 from both sides of the equation.
14x=-1
Divide each term by 14 and simplify.
Divide each term in 14x=-1 by 14.
14×14=-114
Cancel the common factor of 14.
Cancel the common factor.
14×14=-114
Divide x by 1.
x=-114
x=-114
Move the negative in front of the fraction.
x=-114
x=-114
x=-114
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x-1=0
Add 1 to both sides of the equation.
x=1
x=1
The final solution is all the values that make (14x+1)(x-1)=0 true.
x=-114,1
Solve using the Square Root Property 13x+1=14x^2

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